Problem: Jessica is 18 years older than Umaima. Eleven years ago, Jessica was 3 times as old as Umaima. How old is Umaima now?
Answer: We can use the given information to write down two equations that describe the ages of Jessica and Umaima. Let Jessica's current age be $j$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $j = u + 18$ Eleven years ago, Jessica was $j - 11$ years old, and Umaima was $u - 11$ years old. The information in the second sentence can be expressed in the following equation: $j - 11 = 3(u - 11)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = u + 18$ . Substituting this into our second equation, we get the equation: $(u + 18)$ $-$ $11 = 3(u - 11)$ which combines the information about $u$ from both of our original equations. Simplifying both sides of this equation, we get: $u + 7 = 3 u - 33$ Solving for $u$ , we get: $2 u = 40$ $u = 20$.